Abstract
For a finite semilattice S, is is proved that if every noninvertible endomorphism is a product of idempotents, then S is a chain; the converse was proved, independently, by A. Ya. Aĭzenštat and J. M. Howie. For a finite pseudocomplemented semilattice S, with pseudocomplementation regarded as a unary operation, it is proved that all noninvertible endomorphisms are products of idempotents if and only if S is Boolean or a chain.
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More From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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